---
slug: /en/sql-reference/functions/geo/polygons
sidebar_label: Polygons
title: "Functions for Working with Polygons"
---

## WKT

Returns a WKT (Well Known Text) geometric object from various [Geo Data Types](../../data-types/geo.md). Supported WKT objects are: 

- POINT
- POLYGON
- MULTIPOLYGON

**Syntax**

```sql
WKT(geo_data)
```

**Parameters**

`geo_data` can be one of the following [Geo Data Types](../../data-types/geo.md) or their underlying primitive types:

- [Point](../../data-types/geo.md#point)
- [Ring](../../data-types/geo.md#ring)
- [Polygon](../../data-types/geo.md#polygon)
- [MultiPolygon](../../data-types/geo.md#multipolygon)

**Returned value**

- WKT geometric object `POINT` is returned for a Point.
- WKT geometric object `POLYGON` is returned for a Polygon
- WKT geometric object `MULTIPOLYGON` is returned for a MultiPolygon. 

**Examples**

POINT from tuple:

```sql
SELECT wkt((0., 0.));
```

```response
POINT(0 0)
```

POLYGON from an array of tuples or an array of tuple arrays:

```sql
SELECT wkt([(0., 0.), (10., 0.), (10., 10.), (0., 10.)]);
```

```response
POLYGON((0 0,10 0,10 10,0 10))
```

MULTIPOLYGON from an array of multi-dimensional tuple arrays:

```sql
SELECT wkt([[[(0., 0.), (10., 0.), (10., 10.), (0., 10.)], [(4., 4.), (5., 4.), (5., 5.), (4., 5.)]], [[(-10., -10.), (-10., -9.), (-9., 10.)]]]);
```

```response
MULTIPOLYGON(((0 0,10 0,10 10,0 10,0 0),(4 4,5 4,5 5,4 5,4 4)),((-10 -10,-10 -9,-9 10,-10 -10)))
```

## readWKTMultiPolygon

Converts a WKT (Well Known Text) MultiPolygon into a MultiPolygon type.

### Example

``` sql
SELECT
    toTypeName(readWKTMultiPolygon('MULTIPOLYGON(((2 0,10 0,10 10,0 10,2 0),(4 4,5 4,5 5,4 5,4 4)),((-10 -10,-10 -9,-9 10,-10 -10)))')) AS type,
    readWKTMultiPolygon('MULTIPOLYGON(((2 0,10 0,10 10,0 10,2 0),(4 4,5 4,5 5,4 5,4 4)),((-10 -10,-10 -9,-9 10,-10 -10)))') AS output FORMAT Markdown

```
| type | output |
|:-|:-|
| MultiPolygon | [[[(2,0),(10,0),(10,10),(0,10),(2,0)],[(4,4),(5,4),(5,5),(4,5),(4,4)]],[[(-10,-10),(-10,-9),(-9,10),(-10,-10)]]] |


### Input parameters

String starting with `MULTIPOLYGON` 

### Returned value

MultiPolygon

## readWKTPolygon

Converts a WKT (Well Known Text) MultiPolygon into a Polygon type.

### Example

``` sql
SELECT
    toTypeName(readWKTPolygon('POLYGON((2 0,10 0,10 10,0 10,2 0))')) AS type,
    readWKTPolygon('POLYGON((2 0,10 0,10 10,0 10,2 0))') AS output
FORMAT Markdown
```
| type | output |
|:-|:-|
| Polygon | [[(2,0),(10,0),(10,10),(0,10),(2,0)]] |

### Input parameters

String starting with `POLYGON`

### Returned value

Polygon

## readWKTPoint

The `readWKTPoint` function in ClickHouse parses a Well-Known Text (WKT) representation of a Point geometry and returns a point in the internal ClickHouse format.

### Syntax

```sql
readWKTPoint(wkt_string)
```

### Arguments

- `wkt_string`: The input WKT string representing a Point geometry.

### Returned value

The function returns a ClickHouse internal representation of the Point geometry.

### Example

```sql
SELECT readWKTPoint('POINT (1.2 3.4)');
```

```response
(1.2,3.4)
```

## readWKTRing

Parses a Well-Known Text (WKT) representation of a Polygon geometry and returns a ring (closed linestring) in the internal ClickHouse format.

### Syntax

```sql
readWKTRing(wkt_string)
```

### Arguments

- `wkt_string`: The input WKT string representing a Polygon geometry.

### Returned value

The function returns a ClickHouse internal representation of the ring (closed linestring) geometry.

### Example

```sql
SELECT readWKTRing('LINESTRING (1 1, 2 2, 3 3, 1 1)');
```

```response
[(1,1),(2,2),(3,3),(1,1)]
```

## polygonsWithinSpherical

Returns true or false depending on whether or not one polygon lies completely inside another polygon. Reference https://www.boost.org/doc/libs/1_62_0/libs/geometry/doc/html/geometry/reference/algorithms/within/within_2.html

### Example

``` sql
select polygonsWithinSpherical([[[(4.3613577, 50.8651821), (4.349556, 50.8535879), (4.3602419, 50.8435626), (4.3830299, 50.8428851), (4.3904543, 50.8564867), (4.3613148, 50.8651279)]]], [[[(4.346693, 50.858306), (4.367945, 50.852455), (4.366227, 50.840809), (4.344961, 50.833264), (4.338074, 50.848677), (4.346693, 50.858306)]]]);
```
```response
0
```

### Input parameters

### Returned value

UInt8, 0 for false, 1 for true

## polygonsDistanceSpherical

Calculates the minimal distance between two points where one point belongs to the first polygon and the second to another polygon. Spherical means that coordinates are interpreted as coordinates on a pure and ideal sphere, which is not true for the Earth. Using this type of coordinate system speeds up execution, but of course is not precise. 

### Example

``` sql
SELECT polygonsDistanceSpherical([[[(0, 0), (0, 0.1), (0.1, 0.1), (0.1, 0)]]], [[[(10., 10.), (10., 40.), (40., 40.), (40., 10.), (10., 10.)]]])
```
```response
0.24372872211133834
```

### Input parameters

Two polygons

### Returned value

Float64

## polygonsDistanceCartesian

Calculates distance between two polygons

### Example

``` sql
SELECT polygonsDistanceCartesian([[[(0, 0), (0, 0.1), (0.1, 0.1), (0.1, 0)]]], [[[(10., 10.), (10., 40.), (40., 40.), (40., 10.), (10., 10.)]]])
```
```response
14.000714267493642
```

### Input parameters

Two polygons

### Returned value

Float64

## polygonsEqualsCartesian

Returns true if two polygons are equal

### Example

``` sql
SELECT polygonsEqualsCartesian([[[(1., 1.), (1., 4.), (4., 4.), (4., 1.)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]])
```
```response
1
```

### Input parameters

Two polygons

### Returned value

UInt8, 0 for false, 1 for true

## polygonsSymDifferenceSpherical

Calculates the spatial set theoretic symmetric difference (XOR) between two polygons

### Example

``` sql
SELECT wkt(arraySort(polygonsSymDifferenceSpherical([[(50., 50.), (50., -50.), (-50., -50.), (-50., 50.), (50., 50.)], [(10., 10.), (10., 40.), (40., 40.), (40., 10.), (10., 10.)], [(-10., -10.), (-10., -40.), (-40., -40.), (-40., -10.), (-10., -10.)]], [[(-20., -20.), (-20., 20.), (20., 20.), (20., -20.), (-20., -20.)]])));
```
```response
MULTIPOLYGON(((-20 -10.3067,-10 -10,-10 -20.8791,-20 -20,-20 -10.3067)),((10 20.8791,20 20,20 10.3067,10 10,10 20.8791)),((50 50,50 -50,-50 -50,-50 50,50 50),(20 10.3067,40 10,40 40,10 40,10 20.8791,-20 20,-20 -10.3067,-40 -10,-40 -40,-10 -40,-10 -20.8791,20 -20,20 10.3067)))
```

### Input parameters

Polygons

### Returned value

MultiPolygon

## polygonsSymDifferenceCartesian

The same as `polygonsSymDifferenceSpherical`, but the coordinates are in the Cartesian coordinate system; which is more close to the model of the real Earth.

### Example

``` sql
SELECT wkt(polygonsSymDifferenceCartesian([[[(0, 0), (0, 3), (1, 2.9), (2, 2.6), (2.6, 2), (2.9, 1), (3, 0), (0, 0)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]]))
```
```response
MULTIPOLYGON(((1 2.9,1 1,2.9 1,3 0,0 0,0 3,1 2.9)),((1 2.9,1 4,4 4,4 1,2.9 1,2.6 2,2 2.6,1 2.9)))
```

### Input parameters

Polygons

### Returned value

MultiPolygon

## polygonsIntersectionSpherical

Calculates the intersection (AND) between polygons, coordinates are spherical.

### Example

``` sql
SELECT wkt(arrayMap(a -> arrayMap(b -> arrayMap(c -> (round(c.1, 6), round(c.2, 6)), b), a), polygonsIntersectionSpherical([[[(4.3613577, 50.8651821), (4.349556, 50.8535879), (4.3602419, 50.8435626), (4.3830299, 50.8428851), (4.3904543, 50.8564867), (4.3613148, 50.8651279)]]], [[[(4.346693, 50.858306), (4.367945, 50.852455), (4.366227, 50.840809), (4.344961, 50.833264), (4.338074, 50.848677), (4.346693, 50.858306)]]])))
```
```response
MULTIPOLYGON(((4.3666 50.8434,4.36024 50.8436,4.34956 50.8536,4.35268 50.8567,4.36794 50.8525,4.3666 50.8434)))
```

### Input parameters

Polygons

### Returned value

MultiPolygon

## polygonsWithinCartesian

Returns true if the second polygon is within the first polygon.

### Example

``` sql
SELECT polygonsWithinCartesian([[[(2., 2.), (2., 3.), (3., 3.), (3., 2.)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]])
```
```response
1
```

### Input parameters

Two polygons

### Returned value

UInt8, 0 for false, 1 for true

## polygonConvexHullCartesian

Calculates a convex hull. [Reference](https://www.boost.org/doc/libs/1_61_0/libs/geometry/doc/html/geometry/reference/algorithms/convex_hull.html)

Coordinates are in Cartesian coordinate system.

### Example

``` sql
SELECT wkt(polygonConvexHullCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.), (2., 3.)]]]))
```
```response
POLYGON((0 0,0 5,5 5,5 0,0 0))
```

### Input parameters

MultiPolygon

### Returned value

Polygon

## polygonAreaSpherical

Calculates the surface area of a polygon.

### Example

``` sql
SELECT round(polygonAreaSpherical([[[(4.346693, 50.858306), (4.367945, 50.852455), (4.366227, 50.840809), (4.344961, 50.833264), (4.338074, 50.848677), (4.346693, 50.858306)]]]), 14)
```
```response
9.387704e-8
```

### Input parameters

Polygon

### Returned value

Float

## polygonsUnionSpherical

Calculates a union (OR).

### Example

``` sql
SELECT wkt(polygonsUnionSpherical([[[(4.3613577, 50.8651821), (4.349556, 50.8535879), (4.3602419, 50.8435626), (4.3830299, 50.8428851), (4.3904543, 50.8564867), (4.3613148, 50.8651279)]]], [[[(4.346693, 50.858306), (4.367945, 50.852455), (4.366227, 50.840809), (4.344961, 50.833264), (4.338074, 50.848677), (4.346693, 50.858306)]]]))
```
```response
MULTIPOLYGON(((4.36661 50.8434,4.36623 50.8408,4.34496 50.8333,4.33807 50.8487,4.34669 50.8583,4.35268 50.8567,4.36136 50.8652,4.36131 50.8651,4.39045 50.8565,4.38303 50.8429,4.36661 50.8434)))
```

### Input parameters

Polygons

### Returned value

MultiPolygon

## polygonPerimeterSpherical

Calculates the perimeter of the polygon.

### Example

This is the polygon representing Zimbabwe:


```
POLYGON((30.0107 -15.6462,30.0502 -15.6401,30.09 -15.6294,30.1301 -15.6237,30.1699 -15.6322,30.1956 -15.6491,30.2072 -15.6532,30.2231 -15.6497,30.231 -15.6447,30.2461 -15.6321,30.2549 -15.6289,30.2801 -15.6323,30.2962 -15.639,30.3281 -15.6524,30.3567 -15.6515,30.3963 -15.636,30.3977 -15.7168,30.3993 -15.812,30.4013 -15.9317,30.4026 -16.0012,30.5148 -16.0004,30.5866 -16,30.7497 -15.9989,30.8574 -15.9981,30.9019 -16.0071,30.9422 -16.0345,30.9583 -16.0511,30.9731 -16.062,30.9898 -16.0643,31.012 -16.0549,31.0237 -16.0452,31.0422 -16.0249,31.0569 -16.0176,31.0654 -16.0196,31.0733 -16.0255,31.0809 -16.0259,31.089 -16.0119,31.1141 -15.9969,31.1585 -16.0002,31.26 -16.0235,31.2789 -16.0303,31.2953 -16.0417,31.3096 -16.059,31.3284 -16.0928,31.3409 -16.1067,31.3603 -16.1169,31.3703 -16.1237,31.3746 -16.1329,31.3778 -16.1422,31.384 -16.1488,31.3877 -16.1496,31.3956 -16.1477,31.3996 -16.1473,31.4043 -16.1499,31.4041 -16.1545,31.4027 -16.1594,31.4046 -16.1623,31.4241 -16.1647,31.4457 -16.165,31.4657 -16.1677,31.4806 -16.178,31.5192 -16.1965,31.6861 -16.2072,31.7107 -16.2179,31.7382 -16.2398,31.7988 -16.3037,31.8181 -16.3196,31.8601 -16.3408,31.8719 -16.3504,31.8807 -16.368,31.8856 -16.4063,31.8944 -16.4215,31.9103 -16.4289,32.0141 -16.4449,32.2118 -16.4402,32.2905 -16.4518,32.3937 -16.4918,32.5521 -16.5534,32.6718 -16.5998,32.6831 -16.6099,32.6879 -16.6243,32.6886 -16.6473,32.6987 -16.6868,32.7252 -16.7064,32.7309 -16.7087,32.7313 -16.7088,32.7399 -16.7032,32.7538 -16.6979,32.7693 -16.6955,32.8007 -16.6973,32.862 -16.7105,32.8934 -16.7124,32.9096 -16.7081,32.9396 -16.6898,32.9562 -16.6831,32.9685 -16.6816,32.9616 -16.7103,32.9334 -16.8158,32.9162 -16.8479,32.9005 -16.8678,32.8288 -16.9351,32.8301 -16.9415,32.8868 -17.0382,32.9285 -17.1095,32.9541 -17.1672,32.9678 -17.2289,32.9691 -17.2661,32.9694 -17.2761,32.9732 -17.2979,32.9836 -17.3178,32.9924 -17.3247,33.0147 -17.3367,33.0216 -17.3456,33.0225 -17.3615,33.0163 -17.3772,33.0117 -17.384,32.9974 -17.405,32.9582 -17.4785,32.9517 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```

``` sql
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(29.648505, -15.666588), (29.672793, -15.663281), (29.73005, -15.644677), (29.773252, -15.638062), (29.814283, -15.619666), (29.837331, -15.614808), (29.881773, -15.618839), (29.967504, -15.641473), (30.010654, -15.646227)]), 6)
```
```response
0.45539
```

### Input parameters

### Returned value

## polygonsIntersectionCartesian

Calculates the intersection of polygons.

### Example

``` sql
SELECT wkt(polygonsIntersectionCartesian([[[(0., 0.), (0., 3.), (1., 2.9), (2., 2.6), (2.6, 2.), (2.9, 1.), (3., 0.), (0., 0.)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]]))
```
```response
MULTIPOLYGON(((1 2.9,2 2.6,2.6 2,2.9 1,1 1,1 2.9)))
```

### Input parameters

Polygons

### Returned value

MultiPolygon

## polygonAreaCartesian

Calculates the area of a polygon

### Example

``` sql
SELECT polygonAreaCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.)]]])
```
```response
25
```

### Input parameters

Polygon

### Returned value

Float64

## polygonPerimeterCartesian

Calculates the perimeter of a polygon.

### Example

``` sql
SELECT polygonPerimeterCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.)]]])
```
```response
15
```

### Input parameters

Polygon

### Returned value

Float64

## polygonsUnionCartesian

Calculates the union of polygons.

### Example

``` sql
SELECT wkt(polygonsUnionCartesian([[[(0., 0.), (0., 3.), (1., 2.9), (2., 2.6), (2.6, 2.), (2.9, 1), (3., 0.), (0., 0.)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]]))
```
```response
MULTIPOLYGON(((1 2.9,1 4,4 4,4 1,2.9 1,3 0,0 0,0 3,1 2.9)))
```

### Input parameters

Polygons

### Returned value

MultiPolygon

For more information on geometry systems, see this [presentation](https://archive.fosdem.org/2020/schedule/event/working_with_spatial_trajectories_in_boost_geometry/attachments/slides/3988/export/events/attachments/working_with_spatial_trajectories_in_boost_geometry/slides/3988/FOSDEM20_vissarion.pdf) about the Boost library, which is what ClickHouse uses.

